:orphan:
.. _sphx_glr_auto_reliability_sensitivity:
.. _Reliability & Sensitivity:
Reliability & Sensitivity
=========================
.. raw:: html
.. _sphx_glr_auto_reliability_sensitivity_central_dispersion:
.. _Central dispersion:
Central dispersion
------------------
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/central_dispersion/images/thumb/sphx_glr_plot_expectation_simulation_algorithm_thumb.png
:alt: Evaluate the mean of a random vector by simulations
:ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_expectation_simulation_algorithm.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/central_dispersion/plot_expectation_simulation_algorithm
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/central_dispersion/images/thumb/sphx_glr_plot_central_tendency_thumb.png
:alt: Analyse the central tendency of a cantilever beam
:ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_central_tendency.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/central_dispersion/plot_central_tendency
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/central_dispersion/images/thumb/sphx_glr_plot_estimate_moments_taylor_thumb.png
:alt: Estimate moments from Taylor expansions
:ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_estimate_moments_taylor.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/central_dispersion/plot_estimate_moments_taylor
.. raw:: html
.. _sphx_glr_auto_reliability_sensitivity_reliability:
.. _Reliability:
Reliability
-----------
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_estimate_probability_lhs_thumb.png
:alt: Estimate a probability with Latin Hypercube Sampling
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_lhs.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_estimate_probability_lhs
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_event_manipulation_thumb.png
:alt: Simulate an Event
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_manipulation.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_event_manipulation
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_estimate_probability_monte_carlo_thumb.png
:alt: Estimate a probability with Monte Carlo
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_monte_carlo.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_estimate_probability_monte_carlo
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_estimate_probability_randomized_qmc_thumb.png
:alt: Use a randomized QMC algorithm
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_estimate_probability_randomized_qmc
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_estimate_probability_adaptive_directional_sampling_thumb.png
:alt: Use the Adaptive Directional Stratification Algorithm
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_estimate_probability_directional_sampling_thumb.png
:alt: Use the Directional Sampling Algorithm
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_estimate_probability_directional_sampling
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_post_analytical_importance_sampling_thumb.png
:alt: Use the post-analytical importance sampling algorithm
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_post_analytical_importance_sampling.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_post_analytical_importance_sampling
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_flood_model_thumb.png
:alt: Estimate a flooding probability
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_flood_model
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_probability_simulation_parametrization_thumb.png
:alt: Specify a simulation algorithm
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_parametrization.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_probability_simulation_parametrization
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_estimate_probability_importance_sampling_thumb.png
:alt: Use the Importance Sampling algorithm
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_importance_sampling.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_estimate_probability_importance_sampling
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_create_threshold_event_thumb.png
:alt: Create a threshold event
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_create_threshold_event
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_axial_stressed_beam_quickstart_thumb.png
:alt: Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_axial_stressed_beam_quickstart
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_probability_simulation_results_thumb.png
:alt: Exploitation of simulation algorithm results
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_probability_simulation_results
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_multi_form_thumb.png
:alt: Use the FORM algorithm in case of several design points
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_multi_form
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_create_domain_event_thumb.png
:alt: Create a domain event
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_domain_event.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_create_domain_event
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_subset_sampling_thumb.png
:alt: Subset Sampling
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_subset_sampling
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_estimate_probability_form_thumb.png
:alt: Use the FORM - SORM algorithms
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_estimate_probability_form
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_strong_maximum_test_thumb.png
:alt: Test the design point with the Strong Maximum Test
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_strong_maximum_test.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_strong_maximum_test
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_proba_system_event_thumb.png
:alt: Time variant system reliability problem
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_proba_system_event
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_axial_stressed_beam_thumb.png
:alt: Axial stressed beam : comparing different methods to estimate a probability
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_axial_stressed_beam
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_event_system_thumb.png
:alt: Create unions or intersections of events
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_event_system
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability/images/thumb/sphx_glr_plot_form_explained_thumb.png
:alt: An illustrated example of a FORM probability estimate
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_form_explained.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability/plot_form_explained
.. raw:: html
.. _sphx_glr_auto_reliability_sensitivity_reliability_processes:
.. _Reliability processes:
Reliability processes
---------------------
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability_processes/images/thumb/sphx_glr_plot_event_process_thumb.png
:alt: Create an event based on a process
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_event_process.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability_processes/plot_event_process
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/reliability_processes/images/thumb/sphx_glr_plot_estimate_probability_monte_carlo_process_thumb.png
:alt: Estimate a process-based event probability
:ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_estimate_probability_monte_carlo_process.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/reliability_processes/plot_estimate_probability_monte_carlo_process
.. raw:: html
.. _sphx_glr_auto_reliability_sensitivity_sensitivity_analysis:
.. _Sensitivity analysis:
Sensitivity analysis
--------------------
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/sensitivity_analysis/images/thumb/sphx_glr_plot_sensitivity_fast_thumb.png
:alt: FAST sensitivity indices
:ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_fast.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_fast
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/sensitivity_analysis/images/thumb/sphx_glr_plot_sensitivity_par_coo_thumb.png
:alt: Parallel coordinates graph as sensitivity tool
:ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_par_coo
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/sensitivity_analysis/images/thumb/sphx_glr_plot_sensitivity_sobol_multivariate_thumb.png
:alt: Estimate Sobol' indices for a function with multivariate output
:ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol_multivariate.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_sobol_multivariate
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/sensitivity_analysis/images/thumb/sphx_glr_plot_functional_chaos_sensitivity_thumb.png
:alt: Sobol' sensitivity indices from chaos
:ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_functional_chaos_sensitivity.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/sensitivity_analysis/plot_functional_chaos_sensitivity
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/sensitivity_analysis/images/thumb/sphx_glr_plot_sensitivity_ancova_thumb.png
:alt: Use the ANCOVA indices
:ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_ancova.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_ancova
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/sensitivity_analysis/images/thumb/sphx_glr_plot_sensitivity_sobol_thumb.png
:alt: Estimate Sobol' indices for the Ishigami function by a sampling method: a quick start guide to sensitivity analysis
:ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_sobol
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/sensitivity_analysis/images/thumb/sphx_glr_plot_hsic_estimators_ishigami_thumb.png
:alt: The HSIC sensitivity indices: the Ishigami model
:ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/sensitivity_analysis/plot_hsic_estimators_ishigami
.. raw:: html
.. _sphx_glr_auto_reliability_sensitivity_design_of_experiments:
.. _Design of experiments:
Design of experiments
---------------------
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_composite_experiment_thumb.png
:alt: Create a composite design of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_composite_experiment.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_composite_experiment
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_monte_carlo_experiment_thumb.png
:alt: Create a Monte Carlo design of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_monte_carlo_experiment.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_monte_carlo_experiment
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_probabilistic_design_thumb.png
:alt: Probabilistic design of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_probabilistic_design.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_probabilistic_design
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_gauss_product_experiment_thumb.png
:alt: Create a Gauss product design
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_gauss_product_experiment.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_gauss_product_experiment
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_create_random_doe_thumb.png
:alt: Create a random design of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_random_doe.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_create_random_doe
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_mixed_design_thumb.png
:alt: Create mixed deterministic and probabilistic designs of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_mixed_design.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_mixed_design
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_design_of_experiment_continuous_discrete_thumb.png
:alt: Create a design of experiments with discrete and continuous variables
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiment_continuous_discrete.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_design_of_experiment_continuous_discrete
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_plot_design_thumb.png
:alt: The PlotDesign method
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_plot_design
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_deterministic_design_thumb.png
:alt: Deterministic design of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_deterministic_design
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_create_deterministic_doe_thumb.png
:alt: Create a deterministic design of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_create_deterministic_doe
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_low_discrepancy_sequence_thumb.png
:alt: Generate low discrepancy sequences
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_low_discrepancy_sequence
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_design_of_experiments_thumb.png
:alt: Various design of experiments in OpenTURNS
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_design_of_experiments
.. raw:: html
.. only:: html
.. figure:: /auto_reliability_sensitivity/design_of_experiments/images/thumb/sphx_glr_plot_optimal_lhs_thumb.png
:alt: Optimize an LHS design of experiments
:ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py`
.. raw:: html
.. toctree::
:hidden:
/auto_reliability_sensitivity/design_of_experiments/plot_optimal_lhs
.. raw:: html
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-gallery
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download all examples in Python source code: auto_reliability_sensitivity_python.zip `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download all examples in Jupyter notebooks: auto_reliability_sensitivity_jupyter.zip `